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{\huge Project Explanation
}
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In the bus problem in the Minimum Network flow (Min-flow) problem, we construct a network representing the bus route, and, when minimized, the flow $x_{ij}$ on arch $i$-$j$ represents the number of tickets sold under the demand for passenger onboarding the bus from place $i$ heading to destination $j$.

The arches at the bottom of the network ensures the bus is not overloaded with an upper bound $P$. Also, by the nature of the Min-flow problem, fares for bus rides are multiplied by $-1$ to minimized the value that originally should have been maximized.

The graph below represents the minimized min-flow problem after the conversion, where fares (non-zero values) are represented in {\color{ForestGreen} green}, the finite upper bonds on arches are coloured in {\color{blue} blue}, and the differences between inflow and outflow for vertices are presented in black. Without specification, all other parameters are unrestricted (free).

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{\small \textbf{Fig 1}: Bus problem}
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Also, we spotted out that a meeting schedule is similar to a bus service with only one seat ($P=1$), where the attendee is selecting between meetings that resembles selecting a passenger that ``rides" on a one-seater ``bus." Hence, we modify the original problem in suit of the meeting scheduler.

In the modified problem, we define bottom vertices as the start and end of meetings. We define $f_{ij}$ as the values of the meeting from time $i$ to time $j$. Here is the illustration.

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{\small \textbf{Fig 2}: Schedule problem}
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